The human cerebral cortex is topologically equivalent to a sheet and can be
considered topologically spherical if it is closed at the brain stem. Low-
level segmentation of magnetic resonance (MR) imagery typically produces ce
rebral volumes whose tessellations are not topologically spherical. We pres
ent a novel algorithm that analyzes and constrains the topology of a volume
tric object. Graphs are formed that represent the connectivity of voxel seg
ments in the foreground and background of the image. These graphs are analy
zed and minimal corrections to the volume are made prior to tessellation. W
e apply the algorithm to a simple test object and to cerebral white matter
masks generated by a low-level tissue identification sequence. We tessellat
e the resulting objects using the marching cubes algorithm and verify their
topology by computing their Euler characteristics. A key benefit of the al
gorithm is that it localizes the change to a volume to the specific areas o
f its topological defects.